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Mirrors > Home > HOLE Home > Th. List > distrc | Unicode version |
Description: Distribution of combination over substitution. |
Ref | Expression |
---|---|
distrc.1 | |
distrc.2 | |
distrc.3 |
Ref | Expression |
---|---|
distrc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | weq 38 | . 2 | |
2 | distrc.1 | . . . . 5 | |
3 | distrc.2 | . . . . 5 | |
4 | 2, 3 | wc 45 | . . . 4 |
5 | 4 | wl 59 | . . 3 |
6 | distrc.3 | . . 3 | |
7 | 5, 6 | wc 45 | . 2 |
8 | 2 | wl 59 | . . . 4 |
9 | 8, 6 | wc 45 | . . 3 |
10 | 3 | wl 59 | . . . 4 |
11 | 10, 6 | wc 45 | . . 3 |
12 | 9, 11 | wc 45 | . 2 |
13 | 3, 6, 2 | ax-distrc 61 | . 2 |
14 | 1, 7, 12, 13 | dfov2 67 | 1 |
Colors of variables: type var term |
Syntax hints: ht 2 kc 5 kl 6 ke 7 kt 8 kbr 9 wffMMJ2 11 wffMMJ2t 12 |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-trud 26 ax-cb1 29 ax-cb2 30 ax-refl 39 ax-eqmp 42 ax-ceq 46 ax-distrc 61 |
This theorem depends on definitions: df-ov 65 |
This theorem is referenced by: hbc 100 |
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